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A vehicle routing problem with stochastic demand
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A polylogarithmic approximation algorithm for the group Steiner tree problem
Journal of Algorithms
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SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The vehicle routing problem
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STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Approximation algorithms for the covering Steiner problem
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
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Theoretical Computer Science
A Paired-Vehicle Recourse Strategy for the Vehicle-Routing Problem with Stochastic Demands
Transportation Science
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A greedy approximation algorithm for the group Steiner problem
Discrete Applied Mathematics
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IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
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Introduction to Stochastic Programming
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SIAM Journal on Computing
Approximation algorithms for stochastic orienteering
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Technical Note---Approximation Algorithms for VRP with Stochastic Demands
Operations Research
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We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed --- but costs here become more expensive by a factor λ. We present an O(log2n ·log(nλ))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based ω(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.